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Torsion Units in Integral Group Rings

Published online by Cambridge University Press:  20 November 2018

Stanley Orlando Juriaans
Stanley Orlando Juriaans*
Affiliation:
Instituto de Matemática e Estatística Universidade de São Paulo, Caixa Postal 20570, 01452-990-São Paulo, Brasil, e-mail:[email protected]
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Abstract

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Special cases of Bovdi's conjecture are proved. In particular the conjecture is proved for supersolvable and Frobenius groups. We also prove that if is finite, α ∊ VℤG a torsion unit and m the smallest positive integer such that αm ∊ G then m divides .

Keywords

20C0520C0716S3416U60group ringstorsion unitsgeneralized trace
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 317 - 324
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Bovdi, A. A., The Unit Group of Integral Group Rings (Russian), Uzhgorod Univ. 21(1987), Dep. Ukr. Ninti 24.09.87, N2712-UK 87.Google Scholar
2. Bovdi, A., Marciniak, Z. and Sehgal, S. K., Torsion Units in Infinite Group Rings, J. Number Theory 47( 1994), 284–299.Google Scholar
3. Burnside, W., Theory of groups of finite order, 2nd edition, Dover Publication, Inc.Google Scholar
4. Dokuchaev, M. A., Torsion units in integral group ring ofnilpotent metabelian groups, Comm. Algebra (2) 20(1992), 423–435.Google Scholar
5. Gorenstein, D., Finite groups, Harper & Row Publisher, New York, 1968.Google Scholar
6. Juriaans, O. S., Torsion units in integral group ring, Comm. Algebra, to appear.Google Scholar
7. Isaacs, I. M., Character theory of finite groups, Academic Press, New York, San Francisco, London, 1976.Google Scholar
8. Luthar, I. S. and Poonam, T., Zassenhaus Conjecture for S5, preprint.Google Scholar
9. Marciniak, Z., Ritter, J., Sehgal, S. K. and A. Weiss, Torsion units in integral group rings of some metabelian groups, II, J. Number Theory 25(1987), 340–352.Google Scholar
10. Passman, D. S., Permutation groups, W. A. Benjamin, Inc., New York, 1968.Google Scholar
11. Robinson, D. J. S., A course in the theory of groups, Springer-Verlag, New York, Heidelberg, Berlin, 1980.Google Scholar
12. Scott, W. R., Group theory, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964.Google Scholar
13. Suzuki, M., Group Theory II, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1985.Google Scholar
14. Sehgal, S. K., Topics in group rings, Marcel Dekker, Inc., New York and Basel, 1978.Google Scholar
15. Sehgal, S. K., Units of Integral Group Rings, Longman's, Essex, 1993.Google Scholar
16. Weiss, A., Torsion units in integral group rings, J. Reine Angew. Math. 415(1991), 175–187 Google Scholar